Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>Porro præcedentis propoſitionis & corollariorum ejus beneficio,
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                  colligitur etiam proportio vis centripetæ ad vim quamlibet notam,
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                  qualis eſt ea Gravitatis. </s>
                  <s>Nam ſi corpus in circulo Terræ concen­
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                  trico vi gravitatis ſuæ revolvatur, hæc gravitas eſt ipſius vis centri­
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                  peta. </s>
                  <s>Datur autem, ex deſcenſu gravium, & tempus revolutionis
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                  unius, & arcus dato quovis tempore deſcriptus, per hujus Corol. </s>
                  <s>
                    <lb/>
                  IX. </s>
                  <s>Et hujuſmodi propoſitionibus
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                  Hugenius,
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                  in eximio ſuo Tracta­
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                  tu
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                  de Horologio Oſcillatorio,
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                  vim gravitatis cum revolventium vi­
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                  ribus centrifugis contulit. </s>
                </p>
                <p type="main">
                  <s>Demonſtrari etiam poſſunt præcedentia in hunc modum. </s>
                  <s>In cir­
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                  culo quovis deſcribi intelligatur Polygonum laterum quotcunque. </s>
                  <s>
                    <lb/>
                  Et ſi corpus, in polygoni lateribus data cum velocitate movendo,
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                  ad ejus angulos ſingulos a circulo reflectatur; vis qua ſingulis re­
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                  flexionibus impingit in circulum erit ut ejus velocitas: adeoque
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                  ſumma virium in dato tempore erit ut velocitas illa & numerus re­
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                  flexionum conjunctim: hoc eſt (ſi polygonum detur ſpecie) ut longi­
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                  tudo dato illo tempore deſcripta & longitudo eadem applicata ad
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                  Radium circuli; id eſt, ut quadratum longitudinis illius applicatum
                    <lb/>
                  ad Radium: adeoque, ſi polygonum lateribus infinite diminutis co­
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                  incidat cum circulo, ut quadratum arcus dato tempore deſcripti ap­
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                  plicatum ad radium. </s>
                  <s>Hæc eſt vis centrifuga, qua corpus urget cir­
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                  culum: & huic æqualis eſt vis contraria, qua circulus continuo re­
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                  pellit corpus centrum verſus. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO. V. PROBLEMA I.
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                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Data quibuſcunQ.E.I. locis velocitate, qua corpus figuram datam vi­
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                  ribus ad commune aliquod centrum tendentibus deſcribit, centrum
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                  illud invenire.
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                  </s>
                </p>
                <p type="main">
                  <s>Figuram deſcriptam tangant rectæ tres
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                  PT, TQV, VR
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                  in
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                  punctis totidem
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                  P, Q, R,
                    <emph.end type="italics"/>
                  concurrentes in
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  &
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                  V.
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                  Ad tangentes
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                  erigantur perpendicula
                    <emph type="italics"/>
                  PA, QB, RC,
                    <emph.end type="italics"/>
                  velocitatibus corporis in
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                  punctis illis
                    <emph type="italics"/>
                  P, Q, R
                    <emph.end type="italics"/>
                  a quibus eriguntur reciproce proportionalia;
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                  id eſt, ita ut ſit
                    <emph type="italics"/>
                  PA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  QB
                    <emph.end type="italics"/>
                  ut velocitas in
                    <emph type="italics"/>
                  Q
                    <emph.end type="italics"/>
                  ad velocitatem in
                    <lb/>
                    <emph type="italics"/>
                  P,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  QB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  RC
                    <emph.end type="italics"/>
                  ut velocitas in
                    <emph type="italics"/>
                  R
                    <emph.end type="italics"/>
                  ad velocitatem in
                    <emph type="italics"/>
                    <expan abbr="q.">que</expan>
                    <emph.end type="italics"/>
                  Per
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                  perpendiculorum terminos
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                  A, B, C
                    <emph.end type="italics"/>
                  ad angulos rectos ducantur
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                  AD,
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                  DBE, EC
                    <emph.end type="italics"/>
                  concurrentes in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  &
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                  E:
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                  Et actæ
                    <emph type="italics"/>
                  TD, VE
                    <emph.end type="italics"/>
                  concur­
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                  rent in centro qæſito
                    <emph type="italics"/>
                  S.
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                  </s>
                </p>
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